INTEGRAL TAK TENTU
Bentuk umum integral tak tentu yaitu : ∫f(x)dx=f(x)+k
∫ = tanda integral
f(x)dx = diferensial dari f(x)
f(x)+k = fungsi asal
k = konstanta yang nilainya tak tentu
Proses pengintegralan disebut integrasi.
contoh : f(x) = x²+5→f¹(x) = 2x
∫2xdx = x²+kþ
KAIDAH KAIDAH INTEGRAL TERTENTU
Formula pangkat
ʃ xndx = x^(n+1)/(n+1) + k n ≠ -1
contoh: ʃ 3x 2dx = 〖3x〗^(2+1)/(2+1)+k= 3/3 x3 + k = x3 + k
Formula Logaritmik
ʃ 1/x+dx=11n x+k
contoh: ʃ 3/(x+1) dx=3 1n ( x+1 )+k
Formula Eksponensial
ʃ ex dx =ex + k ʃ eu du= eu + k
Contoh: ʃ e2xdx = 1/2 ʃe2x d(2x) = 1/2 e2x + k
ʃ e-3x+2 dx = -1/3 ʃ e-3x-2 d-3x+2= -1/3 e-3x + 2 + k
Formula Penjumlahan
ʃ f(x)+ g(x)dx = ʃf(x)dx+ʃ g(x)dx
= f(x)+g(x)+k
Contoh: ʃ(3×2- 10x)dx= 〖3x〗^(2+1)/(2+1)-〖10x〗^(1+1)/(1+1)+k
= 3/3 x2-10/2 x2+k=x3-5×2+k
ʃ (ex+ 1/x)dx=ex +1n x+k
Formula Subtitusi
ʃ f(u) du/dx dx=ʃ f(u)+x
u= g (x)→ ʃ du= substitusi bagi ʃ dx
Latihan:
(2). ʃ x-4 dx=x^(-4+1)/(-4+1)=-1/3 x-3 + k
(4). ʃ 5x/x dx= ʃ 5x-1dx= 1n x+k
(5). ʃ x2 -√x + 4dx= 1/3 x3 -x^(1/2+1)/(1/2+1)+4x+k=1/3 x^3-2/3 x^(3/2)+4x+k
= 1/3 x^3-2/3 √(x^3 )+4x+k
(6). ʃ √(2+5xdx )= ʃ 〖(2+5x)〗^(1/2) dx= 〖(2+5x)〗^(_2^1)+1 /(1/(2 )+1)+k
Formula perkalian
ʃ nf(x)dx=n ʃ f(x)dx n ≠0
contoh :
ʃ 3×2 dx=3 ʃ x2 dx=3 (x2+1+k)=x3+k 2+1
ʃ-x3 dx=-ʃ x3 dx= -(x3+1+k)=1/4×4±3+1
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